Symmetric & Skew Symmetric Matrix
General
Grade 12
Question:
If $A$ is symmetric as well as skew symmetric matrix, then $A$ is -
diagonal matrix
null matrix
triangular matrix
none of these
Step-by-Step Solution
Key Concept: General
Let $A = [a_{ij}]$ Since $A$ is skew symmetric $a_{ij} = -a_{ji}$ for $i = j, a_{ii} = -a_{ii} \Rightarrow a_{ii} = 0$ for $i \neq j, a_{ij} = -a_{ji}$ [$\because A$ is skew symmetric] and $a_{ij} = a_{ji}$ [$\because A$ is symmetric] $\therefore a_{ij} = 0$ for all $i \neq j$ So, $a_{ij} = 0$ for all '$i$' and '$j$' i.e. $A$ is null matrix.
Correct Answer: B